> Today, I’d like to close this gap with a couple of crisp definitions that stay clear of flawed hydraulic analogies, but also don’t get bogged down by differential equations or complex number algebra.

Related: many, many years ago, when Facebook didn't exist yet, Google still passed as a "good" company, and hobbyist electronic geeks had almost only PICs to choose from, I found online a very long and complete electronic course that went from 0 to basic R/C concepts, to transistors, up to pretty advanced topics like magnets/transformers and IIRC radio too.

It was made of pretty raw HTML pages and images, and what was most peculiar about it was that it managed to explain a lot of concepts up to an applicable level (as in, actually designing analog circuits) without (any?) calculus at all.

Some of those may be false memories, but if I remember correctly:

* Its HTML style had a yellowy background * It was taken from an old-ish (US?) navy electric engineer-focused applied electronics course for training naval engineers. * It was more focused on analog circuits

I remember I downloaded it all but after all those years who knows where it could be. Maybe in some 1GB disk of my first Pentium PC, so it's basically lost.

Does anyone in HN knows what I'm talking about? I was never able to find it again.

[1] https://lcamtuf.substack.com/p/primer-core-concepts-in-elect...

http://compatt.com/Tutorials/NEETS/NEETS.html

Content updated in 2011.

Thank you so much! I've been looking for this for at least fifteen years!

And there are even links to previous HTML versions (this one is PDF)... amazing!

I want to say that’s cool, avoid common pitfalls in explanations, but I want to to point out that all analogies fall short, otherwise they would be the same thing, and not an analogy.

That is, if the hydraulic analogy were perfect, then that would mean that electronics would just behave as a fluid and we could teach it an a part of fluid dynamics.

But instead it is an analogy, electronics is not a part of fluid dynamics, there’s just a few similarities that can be used for teaching.

It’s not unusual to teach an imperfect simplistic model at first that you intend to supplement later with more details that break the analogy.

We can use water to explain why capacitors in series have less capacitance!

I'm now thinking whether we could build a water pressure multiplier using the cascade voltage multiplier topology.

https://en.wikipedia.org/wiki/Voltage_multiplier

Use some rubber dams or flexible pipes for the capacitors, one-way backstop valves for the diodes, and then some back-and-forth pumping mechanism to generate water AC. It should work.

That's the classic way to think about it. Another way is to view the input as simply a sequence of voltage readings. Extracting a useful signal from that is an exercise in exploiting redundancy in noisy data. [1] Software defined receivers work that way.

Analog radio (AM, FM, etc.) is a hulking big carrier weakly modulated by the signal. Analog TV, which was AM video with FM audio, had 80% of the power in the carrier. Analog UHF TV stations often had multi-megawatt transmitters to overpower noise by sheer RF output. Digital broadcast TV transmitters output maybe 150KW, because the modulation is more efficient.

Modern modulation techniques are insanely efficient. It's amazing that mobile phones work.

[1] https://ocw.mit.edu/courses/6-450-principles-of-digital-comm...

I have heard of military radars having megawatts of radiated power. but even then it was in the low megawatts.

https://en.wikipedia.org/wiki/John_R._Brinkley#Brinkley_and_...

Amusingly, over-the-air digital TV is making a comeback. The cable industry pushed prices up too high. But the "comeback" is to only 14% of the viewer base.

[1] https://en.wikipedia.org/wiki/UHF_television_broadcasting

That's the classic way to think about it. Another way is to view the input as simply a sequence of voltage readings."

Right. And modulation of any type produces sidebands as per Fourier! Do anything whatsoever to disturb a pure sine wave then math and physics dictates it so.

There's old modulation techniques that are crazy efficient too - the most obvious one being GPS. A small antenna, just 2cm short [1], is all you need to pick up and distinguish from each other the signal of up to a dozen different GPS and dozens of other (GLONASS, Galileo, BeiDou) navigation satellites. This is mind-blowingly nuts.

For modern high-bandwidth communication, microwave point-to-point links can achieve 65km range with barely 4 watts of RF energy - e.g. German Telekom's Skylink system connecting an aviation radio transmitter on the island of Helgoland with the continental backbone at Cuxhaven [2]. And actually that is way more power than required, half a watt is enough but they chose to go for higher power to achieve perfect reliability even in worst-case conditions [3] (does make sense, given how safety-critical flight radio communication is).

If all you need is satellite communication for a few bytes of information, a cellphone can send an emergency message to satellites anywhere on this planet (at least, where regulatory clearances allow for that) [4].

[1] https://electronics.stackexchange.com/questions/586900/how-c...

[2] https://www.youtube.com/watch?v=q_Ja6QtWwpQ

[3] https://www.telekom.com/de/blog/netz/artikel/skylink-richtfu...

[4] https://support.apple.com/de-de/101573

https://www.youtube.com/watch?v=LMxate9gegg

Basically, imagine a charged shell around the earth that reflects electromagnetic waves back, and that the properties of said shell is constantly fluctuating. Solar storms (and following northern lights) are bad news for radio communication.

That's the very, very ELI5 version.

Although it can allow for auroral backscatter propagation on VHF, which is fascinating. https://www.electronics-notes.com/articles/ham_radio/amateur...

Definitely not good for HF though. The Sun wilding out the past few days has at least given me the opportunity to work on some stuff in the evenings that isn’t screwing around on FT8, lol.

Sounds great! Let’s dig in.

> … the fundamental mirroring behavior is still present, but it’s usually managed pretty well. Accidental mirror images of unrelated transmissions can be mitigated choosing the IF wisely, by designing the antenna to have a narrow frequency response, or by putting an RF lowpass filter in front of the mixer if needs be

Mission failed. Ah well.

The meaning of "mixer" might be inferred from the earlier "the basic operation of almost every radio receiver boils down to mixing (multiplying) the amplified antenna signal with a sine wave of a chosen frequency." And the meaning of "mirroring behavior" might be inferred from the earlier "we can see that every peak of the driving signal reaches the ends of the antenna perfectly in-phase with the bounce-back from the previous oscillation". But these are still explanations that rely on a good amount of past expertise and other jargon not covered in this or the author's other pages, which probably has to involve quite a lot of what most people would consider "advanced math", though as always "advanced" is relative, or alternately a lot of direct experience playing with analog signals.

https://en.wikipedia.org/wiki/Foxhole_radio

> The aerial is connected to the grounded inductor. The coil has an internal parasitic capacitance which, along with the capacitance of the antenna forms a resonant circuit (tuned circuit) with the inductance of the coil, resonating at a specific resonant frequency. The coil has a high impedance at its resonant frequency, and passes radio signals from the antenna at that frequency along to the detector, while conducting signals at all other frequencies to ground. By varying the inductance with a sliding contact arm, a commercial crystal radio can be tuned to receive different frequencies. Most of these wartime sets did not have a sliding contact and were only built to receive one frequency, the frequency of the nearest broadcast station. The detector and earphones were connected in series across the coil, which applied the radio signal of the received radio station. The detector acted as a rectifier, allowing current to flow through it in only one direction. It rectified the oscillating radio carrier wave, extracting the audio modulation, which passed through the earphones. The earphones converted the audio signal to sound waves.

In conclusion, you should be able to build a simple radio from copper wire, aluminium foil, a pencil, a razor blade, and baking powder.

[1] https://en.wikipedia.org/wiki/Crystal_radio

[2] https://en.wikipedia.org/wiki/Crystal_earpiece

[3] https://en.wikipedia.org/wiki/Foxhole_radio

[4] https://en.wikipedia.org/wiki/Potassium_sodium_tartrate

[5] https://rimstar.org/science_electronics_projects/index.htm#S...

The idea behind this demodulator is quite easy: the diode filters out all of the negative part of the signal, then the positive signal charge the capacitor and the energy is released in a quite constant way (R*C must be several order of magnitude higher than 1/f where f is the carrier frequency) during the negative signal "hole".

A classic passive RC or LC or RL filter, will cause a phase shift. Take the difference between two phases effectively decodes FM. No active elements required. With only RL filters it would be very inefficient. So you may need to be standing next to the transmitter if you don't have at least one transistor or tube. But one such tube or transistor would be plenty for a strong local broadcast.

If you have some capacitors, it gets easier. Maybe paper and tinfoil rolled tightly, or flakes of glass or mica between thin slices of wood. Check out the slope detector circuits here [1] (fig 3, 4); the article is a good introduction to FM detection in general.

[1] https://wiki.analog.com/university/courses/electronics/elect...

NFC (eg. Apple Pay) is a radio, range a few cm. Bluetooth is a radio, a few meters. WiFi is several radio systems, range tens of meters. Cell phone is several radio systems, range up to kilometers. GPS (and rival systems) range up to thousands of kilometers.

> As with proximity card technology, NFC uses inductive coupling between two nearby loop antennas effectively forming an air-core transformer. Because the distances involved are tiny compared to the wavelength of electromagnetic radiation (radio waves) of that frequency (about 22 metres), the interaction is described as near field. An alternating magnetic field is the main coupling factor and almost no power is radiated in the form of radio waves (which are electromagnetic waves, also involving an oscillating electric field); that minimises interference between such devices and any radio communications at the same frequency or with other NFC devices much beyond its intended range. NFC operates within the globally available and unlicensed radio frequency ISM band of 13.56 MHz. Most of the RF energy is concentrated in the ±7 kHz bandwidth allocated for that band, but the emission's spectral width can be as wide as 1.8 MHz[57] in order to support high data rates.

https://en.m.wikipedia.org/wiki/Near-field_communication

It is if you encode information by switching it on and off in standard patterns. These uniform waveforms--or "continuous wave" (CW)--allow very simple devices with very little RF power to be used to communicate with Morse Code.

An even less intuitive result is that you can decode a signal that is weaker than the noise floor if the data rate is sufficiently low and/or the bandwidth is sufficiently high. This has practical applications in amateur modes like JT65, ultra-wideband communications and even GPS.

The noise is effectively AM, since you are modulating the signal from 0 to full amplitude, and with the very fast amplitude change you get what looks like characteristic AM signal with a center carrier and symmetric sidebands.

[1] https://imgur.com/BnagQzb.jpg

That said, a receive antenna does absolutely have "gain", which is evident by the antenna receiving a stronger or weaker signal depending on its orientation with respect to the transmit antenna. The key is this: for an arbitrary antenna, the (transmit, if you like) gain has a one-to-one relationship to the "effective receive area" at a given frequency, so talking about area and gain are equivalent, if not intuitive. We usually assume for point-to-point links that the antennas are oriented at each other, and in such cases (for good aperture antennas), you are absolutely right that the physical area and effective area are approximately equal. For ideal wire antennas, however, the physical area of the antenna is 0, but the effective area is nonzero (because of magic).

Now, I disagree that the path loss equation violates conservation of energy. The link to the effective area and gain depends on the wavelength. When I increase the frequency of operation but I keep the gain of the antennas constant, the areas decrease, so my receive antenna is physically smaller and the power goes down. Not breaking physics. A lot of people will say "path loss gets worse as you go up in frequency", and this is extremely misleading if not "scientifically illiterate" as you pointed out. Sure, there are molecular absorption bands from oxygen/water that literally dissipate power in the atmosphere, but generally speaking, the path loss didn't get worse, your receive antenna just got smaller.

Now wait a minute, what if I just made my receive antenna larger? Well, you can do that! The problem is that because gain and area are linked, efficiently receiving power in a given LARGE area (with respect to the wavelength) implies high gain. High gain implies a very narrow beam (more like a laser pointer than a normal dipole spilling energy everywhere). So it becomes really important that I "point" my receive antenna perfectly at the transmitter. Satellite dishes are really big, and they absolutely have to be pointed accurately at the satellite.

With path loss equation I assume you refer to Friis equation which is just the ratio of power received at an antenna to power given to the transmitter. It is correct and does not violate conservation of energy since it says nothing about the power not received at the receiver

Now here's the catch: If the receive area were not changing as a function of frequency when the receive antenna gain is kept constant (it does), this would break physics (it doesn't). However, the effective area of an antenna with fixed gain varies as 1/lambda^2. In effect the geometric interpretation is still correct, but the variation of antenna area with gain resolves the seeming paradox and saves physics.

I think nobody says that is does. I believe the problem is to call Friis transmission equation "Free-space loss". Actually the Friis formula is composed of 3 terms: the receiving and transmitting antennas gain and the actual free space loss which has the 1/R^2 dependency (which actually isn't a "loss" in energy balance terms, since it's not lost energy, just energy not received at a certain point, so we could argue about that term too...)

Well, it depends on one's definition of gain! If you were to say to the designers of the ELT (the Extremely Large Telescope) that it had no gain over isotropic then they'd fall about laughing (remember, its method of operation also relies on collecting and concentrating incoming EM radiation as do RF antennae). An antenna's effective gathering aperture and directivity for both RX and TX is just about everything, and the coupling efficiency from the antenna to the feeder and RX/detector, and vice versa for the TX just about covers the rest.

"...though the transmitting antenna can have gain depending on shape and size."

Uh? How? What's the difference? Physics says the law of reciprocity applies, a good transmitting antenna also makes just as good a receiving antenna. The only proviso being that a transmitting antenna has to be designed to withstand high RF power levels (even then, this only applies to TX power levels where I²R losses can cause enough heating to damage the antenna and feed lines, similarly, high power TX levels can lead to very high voltages which can arc over; TX antennae are designed to handle this.)

I used to work with microwave transmitters and receivers and my microwave dishes and other types of antennae were directly interchangeable—in fact, they were identical.

Re the Path Loss Equation, it works in the practical sense and is used everywhere. Fighting over technicalities here is akin to arguing the difference between laws of motion under Newton and when they're subject to the rules of Einstein's Relativity. It's damn obvious when one's applicable and the other is not.

Why is that?

Where the "bogus" gain really shines, though: I can take my original receive antenna, operate it as a transmitter (so gain is now relevant), receive with my original transmit antenna (where I now care about area) and get the exact same result in terms of loss!

So many issues come about by taking these for granted. EMF interference , a short circuit or a noisy power supply can cause non-deterministic issues that will drive you mad unless you are aware of the root cause.

He said that he got his phd because that’s pretty much how long it took him before he felt like he really understood how his radio worked, and even then sometimes wasn’t sure.

Was a good speech that this article reminded me of.

Most of the time when people try to explain antenna's they start talking resonance. Which really describes a 'good' antenna.

What an antenna does is create a alternating magnetic field with a alternating electric field 90 degress out of phase with each other. Blah blah blah quantum electrodynamics blah blah blah radiates photons.

Resonance means the antenna stores energy as resonance. That increases the electric and magnetic fields making the antenna radiate more efficiently. Some antenna's are very wide band and 'flat' and used for cough cough military cough cough and other applications.

There is A LOT of money to be made in the space, if you're good.

But, it's not AdTech, so HN isn't familiar with the field I guess :^)

How do you know? For instance, I'd suggest that not every method of modulation has been invented or even yet implemented. Also, we've hardly begun to design and implement meta materials into antennae and RF filters—the field's still wide open for innovation and invention.

And new methods of 'machining' steel have recently been invented and are just coming into use (if I owned the patents I'd be sitting pretty for life).

Consider the fight between a company that's great at RF design, and a company that's on top on software. Which do you think will win in the market for cell phones? (This is a trick question.)

Mature technologies tend to be things that can be outsourced. So one can make some money (if not a lot) as a supplier of these things in a horizontally integrated industry.

Re cell phones, I'll just say this. RF engineering went through a revolution about 10 to 15 years before cell phones became commonplace. The electronics shrunk in size by an order of magnitude, the RF front ends including its transistors increased their FT (transition/cutoff frequency) by over an order of magnitude, and the noise figure of RF front ends was reduced to well below 1dB.

The net/combined result of these three improvements in RF engineering was a truly remarkable achievement. Fact is, there'd be no smartphones or integrated GPS without these developments all having happened. I'd also add that by and large programmers simply haven't a clue about this very special aspect of RF engineering. They just take for granted that the hardware does what it says, to them it's just a black box.

Programming, which cannot be really called engineering because many decades on, it's still an undisciplined way of working that's more akin to an art form than true professional engineering, can however provide the glitz factor that sells phones, but it's completely lost without the state-of-art RF hardware substrate upon which it sits. Moreover, the next revolution in phone technology such as direct satellite services, will only be practical after a further revolution in RF hardware (what passes for some showy demos today is nowhere near the mark if the tech is to be widely adopted).

If you think I've been too hard on programming then I'd suggest you read this near 30-year-old SciAm article as starting point: https://www.researchgate.net/publication/247573088_Software'....

Thirty years on essentially programming has adopted some new techniques for developing software but the fundamental underlying problem of the lack of rigorous standards together with proven methods to solve problems by computer remains unresolved, and in some instances the software industry has gotten demonstrably worse.

I've not the time to put current references that support my claim but a search will soon find them—ones written by both authoritative people within the programming industry and elsewhere such as in computer science research.

Edwin Armstrong was a brilliant brilliant man.

Armstrong definitely was a genius though. Before the superheterodyne receiver he also invented the regenerative receiver.

And you're right, the superheterodyne is such a marvelous technology. The principles it's based on aren't super complex in itself, but the combination of them is genius.

https://en.wikipedia.org/wiki/Regenerative_circuit https://en.wikipedia.org/wiki/Superheterodyne_receiver

"Edwin Armstrong was a brilliant brilliant man."

Right! ...And as you'd likely know, Armstrong's tormentor and nemesis was an arrogant, despicable bastard of the first order!

(Believe it or not, but decades ago I worked in a prototype lab at RCA and actually met David Sarnoff albeit briefly. That never changed my opinion of him.)

So, you worked for RCA.. here is a question that there is no good book on, but what killed RCA, and what was it like working there?

I dont know what I think of Sarnoff - not sure I'd use evil - he was a "no niceties" fiercely competitive capitalist for sure - and how you feel about that may vary, Armstrong was also an extremely hard headed man, and thats not something that result in successful litigation - even if I am normally biased towards the underdog, he isn't always the most sympathetic underdog.

Say we have the technology to broadcast a signal from an antenna to receivers, with some bandwidth B. Without getting clever, we can only send or receive one signal, since any others would interfere with each other.

The trick is, can we do something to shift the bandwidth B to some other base frequency F such that B + F > B? Or B + (N - 1)F > B? And if we can do that, and then downshift from B + NF back to B, it means we can broadcast to multiple channels, and receivers can tune their antennas to F and downshift the decoded signal to 0 and receive it at the original bandwidth B.

A cheap way to do this is amplitude modulation, where multiplying a signal with bandwidth B by a carrier signal of frequency F shifts it up to the range F +/- B and we can space channels apart by 2B to get however many channels our antennas allow for.

The real question is, why is it 2B and not B? Well that lies in some Fourier analysis, where the bandwidth of a signal extends into negative frequency ranges. But neverless, there is another trick, called single-side-band modulation (SSB) where we can shift a signal into the range F + B instead of F +/- B, and demodulate it into -B, B to get the original.

And that gets us to the 1950s in terms of radio technology.

The trick behind FM is to understand we can get more bandwidth by shifting the frequency response not into a series of non-overlapping channels centered at carrier frequencies like AM, but to distribute most of the information across many non overlapping bands over the entire spectrum of the antennas. To do this we don't modulate the amplitude of the carrier, but its frequency. This makes it possible to distribute far more bandwidth across a wide range of frequencies, and it's how FM radio works today.

These concepts create the foundation for modern radio communication, We can modulate data signals to different bandwidths and receive them, provided we know where to tune to. And these bandwidths can either be continuous chunks of spectrum (AM), or interleaved (FM). The next step is to think in terms of time, which is to say that we can have receivers negotiate not only which ranges in frequency they care about, but which time frames they want to listen before waiting for their next time slot.

For those interested in the theory, the fundamental problem is that we can design antennas that can transmit or receive at some fixed maximum bandwidth, bounded by physics. The engineering problem is to find out how to share that bandwidth to maximize the number of receivers and/or senders by sharing the same bandwidth. Amplitude modulation is excellent, but it divides the bandwidth up into a fixed number of channels of maximum individual bandwidth. FM is a bit more efficient in how it can allow many broadcasters to even more receivers choose which channels they receive. But for modern communications, where we need high bandwidth for distinct transmitter/receiver connections, we need protocols to figure out how to share the bandwidth over the air and the two tricks are to divide that bandwidth by frequency (like AM and FM) or time (sharing the same frequency channels, but only picking the frames that we care about), or both.

The answer is C = Blog2(1 + S/N) where B is the bandwidth and S/N is the signal to noise ratio determined by the environment (how much noise is present relative to the signal being transmitted). The crazy thing is this was proven in the 1940s and everyone interested should go read The Mathematical Theory of Communication by Claude Shannon. This is referred to as the Shannon-Hartley theorem, and it determines the channel capacity (C, in bits/second) of any communication channel in the presence of noise.

The math concepts might seem heady, but it's actually fairly approachable and available online. It's fascinating that the fundamentals were proven out in one work nearly 80 years ago by a handful of people, and the math is not that bad.

The thing that makes this nuts is that if an engineer picks some target bitrate for a device, say a cellphone watching video, they can work backwards to determine the channel capacity they need, do some experiments to figure out noise, and then determine what the target their modem protocol needs to reach to be suitable. And this is how we get 5G and fiber or whatever comes next.

https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_a...

https://spectrum.ieee.org/claude-shannon-information-theory

One of the all time greats.

Ah. The real magic is when we separate by space (beyond just frequency or time). The ability to do this was discovered relatively recently, in 1996, by a guy called Foschini, though radio astronomers will say "Meh". By adding multiple antennas and doing space-time coding engineers found they could pump an order of magnitude more data through a radio channel. The maths involved is high school level (linear simultaneous equations), and it's magic to understand Foschini's work and think "Why didn't we do that before?"

The other bit of radio magic is error control coding. This is the stuff that lets us reliably talk to Voyagers I and II.

From the Wikipedia article:

> can thus access a potentially unbounded set of states

That's what people originally thought about MIMO. MIMO's not unbounded. The limit to the number of states is related to the surface area of the volume enclosing the antenna, with the unit of distance being the wavelength. A result radio astronomers already knew when the comms people derived it. With absolutely no evidence to back it up, I'd guess that the same limit applies to OAM multiplexing.

As an aside, when one expresses physics in terms of information theory my understanding is that the maximum the number of bits that can be stored in a volume of space (also the number of bits requited to completely describe that volume of space) is related to the surface area of the volume with the linear unit being Plank lengths. Is MIMO capacity in some way a fundamental limit in communications?

[1] https://physics.stackexchange.com/questions/497475/can-anyon...

I don't believe radiocommunications and the electronics of radio is hard to understand—at least that's so at a level where a hobbyist can gain enjoyment from the subject.

I say that as someone who obtained a radio amateur's license in junior highschool at age 15.

Yes, radio engineering and its physics does get very complicated at the high end, and for a good understanding one requires advanced math including partial differential equations such Maxwell's equations and their SR/Special Relativity extensions, and beyond that one needs to understand the physics of electrodynamics and that requires knowledge of quantum mechanics including QFT (Quantum Field Theory), which is top-echalon physics and close to as complex as physics gets.

However, the hobbyist doesn't need to know an iota of that advanced complex stuff to enjoy radio as a hobby. Absolutely none of it.

All that he/she needs to know are very basic principles such as how antennas receive and radiate signals, how radio signals are amplified and detected, and later on how signals are mixed, multiplied and hetrodyned, and how radio transmitters and receivers work—even the principles behind how the common superhetrodyne receiver works is pretty standard knowledge for a radio hobbyist.

Back when I was learning about radio I doubt very much if an article would have been written in the tone of this story, especially so one that implied that to understand the subject could be difficult even at a hobby level. Why, you may ask? Well back then, if anyone had a hobby interest in electricity and electronics then essentially the only outlet for their interest was radio and perhaps television, as the other branches of electronics would not have been as readily accessible to hobbyists.

Nowadays, that's changed, there's much more to keep a hobbyist's interests such as programming, computers, computer games, and other electronics not based on radio technology—digital electronics for instance, so knowledge about radio tech and radiocommunications theory have become much less commonplace having been diluted amongst all these competing interests. Obviously, the knowledge is still out there but it's more widely dissipated and not as easily accessible in the practical sense, especially so for hobbyists of a young age.

When radio was essentially all that there was around there were many more elementary books on radio available for younger readers and these increased in complexity as the hobbyist gained practical experience. For instance, when I first became interested in radio my first introduction to the subject—like most others—was building crystal set radios, and from there we advanced to incorporating tubes and transistors into our more advanced designs. For beginners, hands-on practical books such as how to build crystal sets which included many different designs were commonly available.

(Back then, a well known author of books on crystal sets and basic radio was Bernard B. Babani, an unforgettable name if ever there was one. His books are still available but you'd never know to look for them unless told about them.)

Today, many have never heard of crystal sets let alone their 'cats' whisker' detectors, so when they become interested in the subject they're thrown in at the deep end. And not having the basics already under their belts, the more advanced radio theory comes as a bit of a shock.